Figure REF  shows the performance curves for the quantum turbo codes studied in [1]}, [2]} operating over the static and TV channels. Here we use \(p\)  instead of \(\gamma \) , since the depolarizing channel is considered (calculating the depolarizing probability of a CTA associated to a value of \(\gamma \)  is trivial). This code has rate \(R_\mathrm {Q}=1/9\) , a block length of 1000 qubits, and is decoded using the turbo decoding algorithm presented in [3]}, [4]}, which combines two Soft-In Soft-Out (SISO) decoders. From this figure, it can be observed that the performance degradation for the QTC when the channel is the TVADCTA rather than the static ADCTA begins at the waterfall region and becomes more prominent as the depolarizing probability decreases. For example, for a depolarizing probability \(p\approx 0.12\) , the Word Error Rate, \(\mathrm {WER}\) , of the QTC operating over the static channel is within the range of \(\mathrm {WER} \approx 10^{-2}\) , but for that same \(p\) , it increases an order of magnitude to \(\mathrm {WER} \approx 10^{-1}\)  when operating over the TV channel scenario QA_C6. This \(\mathrm {WER}\)  deviation increases almost four orders of magnitude when the depolarizing probability decreases to \(p\approx 0.1\)  for the same superconducting qubit scenarios. Thus, as concluded in [2]}, the fluctuations of the relaxation time of the superconducting qubits substantially worsen the error correcting capabilites of the QECCs.
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